- Email: [email protected]
Linear robust control
1788
Book Reviews
Learning the PSP requires the completion of at least ten projects (five to ten hours per project). An engineer probably needs a year of practice for the PSP to become second nature. Reading the book and then trying to apply it to your job will not work. Htnnphrey's book is not theory; it is practical. He gives numbers from dozens of his and his students' personal projects that show that these methods work, This is the strength of the book, and what separates it from most books about software. It gives methods proven by practice--not someone's idea of what should work. The book requires time, commitment, and work. My experience says it is worth it. I now complete my personal projects more quickly, with higher-quality results.
Linear Robust Control, by Michael GREEN and David J.N. LIMEBEER; Prentice Hall Information and System Sciences Series; Prentice Hall; Englewood Cliffs, NJ, USA; 1995; 538 pp.; $76; ISBN" 0-13-102278-4
Reviewed by: Tadeusz KACZOREK Warsaw University of Technology, Warsaw, Poland Roughly speaking, systems are called "robust" ffthey can tolerate plant variability and uncertainty. The main goal of this book is to present a feedback system analysis and synthesis that optimize the performance and robustness of control systems. The authors aim to present the theory in a way which may be accessible to engineers. The book consists of twelve chapters and two appendices. Chapter 1 introduces the goals and origins of H m optimal control. The main ideas are shown on simple scalar examples, which are solved using Nevanlinna-Pick-Schur interpolation theory. Chapter 2 deals with the application of singular values in multivariable control-system design, and a generalization of the Nyquist stability theory for multivariable systems. Singular value inequalities, sensitivity operators, disturbance alternation and tracking are also considered. Basic definitions and properties of signals and systems and the small-gain theorem are given in Chapter 3. The small-gain theorem states that stable systems can be connected to form a stable closedloop, ff the loop gain product is less than unity. Chapter 4 deals with linear fractional transformations and their role in control systems. The linear fractional tran~ormations provide a useful general framework for controller synthesis and computational software.
In the next four chapters, the control system synthesis theory is developed. In Chapter 5 the connections between H °" optimal control and the linear quadratic Gaussian theory is clarified. Both finitehorizon and infinite-horizon optimization problems are considerecL Chapters 6, 7 and 8 are the core of the book, and concentrate on the synthesis of controllers that meet H ~ norm objectives. It is shown that there exists a controller satisfying the objectives if, and only if, two suitable Riccati equations have appropriate solutions. In Chapter 6 the full-information H °+ controller synthesis for a finite horizon and for an infinite horizon is presented. An estimation dual to the fullinformation H ~° control problem is considered in Chapter 7. The H ® filtering problem is transformed into an equivalent H ~ control problem with full disturbance information. The H ~ Wiener filtering problem is discussed. Chapter 8 deals with the H ~ generalized regulator problem; it is shown that all solutions to the H ~ generalized regulator problem have the form of an H °° filter that estimates the fullinformation H ~ control law. The problem of the approximation of high-order systems by others of lower order (model reduction) is developed in the next three chapters. Model reduction by truncation is considered in Chapter 9. Truncation methods of model reduction seek to remove or "tnmcate" unimportant states from state-space models. An optimal (H~nkel norm approximation) model reduction is discussed in Chapter 10. Chapter 11 deals with the four-block problem and the frequency weighted model reduction problem. It is shown that the optimal solution of the four-block problem enables a complete solution of the optimal H °° controller synthesis. In Chapter 12 the design techniques are applied to the stabilization of the vertical dynamics of the elongated plasma in a tokamak, and the design of a product-composition controller for a high-purity distillation column. Internal stability problems and the parametfization of all stabilizing controllers are considered in Appendix A. A brief development of H ~° synthesis for discrete-time systems is given in AppendixB. The material of this book is well-selected and wellorganized. The style is clear, concise and readable. The many well-chosen examples illustrate the theoretical considerations very clearly. This excellent book is addressed to undergraduate and graduate students who have some basic knowledge of linear algebra, matrix theory, linear differential equations and classical and optimal control theory. It can be also recommended to engineers engaged in controlsystem design and development.
Book Reviews
Learning the PSP requires the completion of at least ten projects (five to ten hours per project). An engineer probably needs a year of practice for the PSP to become second nature. Reading the book and then trying to apply it to your job will not work. Htnnphrey's book is not theory; it is practical. He gives numbers from dozens of his and his students' personal projects that show that these methods work, This is the strength of the book, and what separates it from most books about software. It gives methods proven by practice--not someone's idea of what should work. The book requires time, commitment, and work. My experience says it is worth it. I now complete my personal projects more quickly, with higher-quality results.
Linear Robust Control, by Michael GREEN and David J.N. LIMEBEER; Prentice Hall Information and System Sciences Series; Prentice Hall; Englewood Cliffs, NJ, USA; 1995; 538 pp.; $76; ISBN" 0-13-102278-4
Reviewed by: Tadeusz KACZOREK Warsaw University of Technology, Warsaw, Poland Roughly speaking, systems are called "robust" ffthey can tolerate plant variability and uncertainty. The main goal of this book is to present a feedback system analysis and synthesis that optimize the performance and robustness of control systems. The authors aim to present the theory in a way which may be accessible to engineers. The book consists of twelve chapters and two appendices. Chapter 1 introduces the goals and origins of H m optimal control. The main ideas are shown on simple scalar examples, which are solved using Nevanlinna-Pick-Schur interpolation theory. Chapter 2 deals with the application of singular values in multivariable control-system design, and a generalization of the Nyquist stability theory for multivariable systems. Singular value inequalities, sensitivity operators, disturbance alternation and tracking are also considered. Basic definitions and properties of signals and systems and the small-gain theorem are given in Chapter 3. The small-gain theorem states that stable systems can be connected to form a stable closedloop, ff the loop gain product is less than unity. Chapter 4 deals with linear fractional transformations and their role in control systems. The linear fractional tran~ormations provide a useful general framework for controller synthesis and computational software.
In the next four chapters, the control system synthesis theory is developed. In Chapter 5 the connections between H °" optimal control and the linear quadratic Gaussian theory is clarified. Both finitehorizon and infinite-horizon optimization problems are considerecL Chapters 6, 7 and 8 are the core of the book, and concentrate on the synthesis of controllers that meet H ~ norm objectives. It is shown that there exists a controller satisfying the objectives if, and only if, two suitable Riccati equations have appropriate solutions. In Chapter 6 the full-information H °+ controller synthesis for a finite horizon and for an infinite horizon is presented. An estimation dual to the fullinformation H ~° control problem is considered in Chapter 7. The H ® filtering problem is transformed into an equivalent H ~ control problem with full disturbance information. The H ~ Wiener filtering problem is discussed. Chapter 8 deals with the H ~ generalized regulator problem; it is shown that all solutions to the H ~ generalized regulator problem have the form of an H °° filter that estimates the fullinformation H ~ control law. The problem of the approximation of high-order systems by others of lower order (model reduction) is developed in the next three chapters. Model reduction by truncation is considered in Chapter 9. Truncation methods of model reduction seek to remove or "tnmcate" unimportant states from state-space models. An optimal (H~nkel norm approximation) model reduction is discussed in Chapter 10. Chapter 11 deals with the four-block problem and the frequency weighted model reduction problem. It is shown that the optimal solution of the four-block problem enables a complete solution of the optimal H °° controller synthesis. In Chapter 12 the design techniques are applied to the stabilization of the vertical dynamics of the elongated plasma in a tokamak, and the design of a product-composition controller for a high-purity distillation column. Internal stability problems and the parametfization of all stabilizing controllers are considered in Appendix A. A brief development of H ~° synthesis for discrete-time systems is given in AppendixB. The material of this book is well-selected and wellorganized. The style is clear, concise and readable. The many well-chosen examples illustrate the theoretical considerations very clearly. This excellent book is addressed to undergraduate and graduate students who have some basic knowledge of linear algebra, matrix theory, linear differential equations and classical and optimal control theory. It can be also recommended to engineers engaged in controlsystem design and development.